Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
4th Edition
ISBN: 9781337687805
Author: James Stewart
Publisher: Cengage Learning
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Question
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Chapter G, Problem 2E

(a)

To determine

To calculate:

The partial fraction decomposition equation for the following function:

  xx2+x−2

(a)

Expert Solution
Check Mark

Answer to Problem 2E

The partial fraction decomposition equation of xx2+x−2 is

  A(x−1)+B(x+2) .

Explanation of Solution

Given information:

  xx2+x−2

Calculation:

The equation is:

  xx2+x−2

First simplify the given equations as:

  xx2+x−2=xx2+2x−x−2xx2+x−2=xx(x+2)−1(x+2)xx2+x−2=x(x+2)(x−1)

Need to convert the above equation in the form of partial fraction decomposition:

  x(x+2)(x−1)=A(x−1)+B(x+2)xx2+x−2=A(x−1)+B(x+2)

(b)

To determine

To calculate:

The partial fraction decomposition equation for the following function:

  xx2+x+2

(b)

Expert Solution
Check Mark

Answer to Problem 2E

The partial fraction decomposition equation of xx2+x+2 is

  A(x−1)+B(x+2) .

Explanation of Solution

Given information:

  xx2+x+2

Calculation:

The equation is:

  xx2+x+2

First simplify the given equations as:

  xx2+x−2=xx2−2x−x−2xx2+x−2=xx(x−2)+1(x−2)xx2+x−2=x(x−2)(x+1)

Need to convert the above equation in the form of partial fraction decomposition:

  x(x−2)(x+1)=A(x+1)+B(x−2)xx2+x+2=A(x−1)+B(x+2)

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Chapter G, Problem 1E
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Chapter G, Problem 3E

Chapter G Solutions

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

Ch. G - Prob. 1ECh. G - Prob. 2ECh. G - Prob. 3ECh. G - Prob. 4ECh. G - Prob. 5ECh. G - Prob. 6ECh. G - Prob. 7ECh. G - Prob. 8ECh. G - Prob. 9ECh. G - Prob. 10E
Ch. G - Prob. 11ECh. G - Prob. 12ECh. G - Prob. 13ECh. G - Prob. 14ECh. G - Prob. 15ECh. G - Prob. 16ECh. G - Prob. 17ECh. G - Prob. 18ECh. G - Prob. 19ECh. G - Prob. 20ECh. G - Prob. 21ECh. G - Prob. 22ECh. G - Prob. 23ECh. G - Prob. 24ECh. G - Prob. 25ECh. G - Prob. 26ECh. G - Prob. 27ECh. G - Prob. 28ECh. G - Prob. 29ECh. G - Prob. 30ECh. G - Prob. 31ECh. G - Prob. 32ECh. G - Prob. 33ECh. G - Prob. 34ECh. G - Prob. 35ECh. G - Prob. 36ECh. G - Prob. 37ECh. G - Prob. 38ECh. G - Prob. 39ECh. G - Prob. 40ECh. G - Prob. 41ECh. G - Prob. 42ECh. G - Prob. 43ECh. G - Prob. 44ECh. G - Prob. 45ECh. G - Prob. 46E
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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY